70975

General Formulae for Energy Change

In the light of the results discussed in the last two sections we will postulate that the generał expression for the change in stored energy in an electromagnetic system in response

to changes in fields is

dU=

z

v{E • dD+H- dB}dv (7.7)

This generał result is, in simple situations amenable to analysis, in accord with theoretical

results based on Maxwell's equations and the force law, and in morę complex geometries is in accord with experiments, and will thus be regarded as a correct statement

in all cases of the changes in stored energy in an electromagnetic field.

Because it is very convenient to regard the energy as actually stored within the field, we will remove the integration and say that at any point the change in energy stored per

unit volume in a field, when the field changes, is dW= E • dD+H- dB (7.8)

where W denotes the energy stored per unit volume of space at a point at which the field vectors appearing in the equation above apply.

If we divide by an incremental time dtover which the energy change has taken place and proceed to the limit, recognising the independence of both the space and time variables, we obtain

aw

at

= E • dD

at

+H-

dB

at

•(7.9)

This is the fundamental equation